Graphics Development Control and Analysis Process Capability Based Distribution Beta Binomial

DOI

10.2991/icomse-17.2018.18How to use a DOI?

Keywords

Binomial, Beta Binomial Distribution, Control Charts, Process Capability Analysis

Abstract

The proportion of a product defect is usually considered to be fixed, so as to control the quality of a product defect proportions using p control chart (based Binomial), but not necessarily the proportion of a product defect fixed (same), but having such distribution Beta distribution, it is often the case when in the production process of a product contained in the shift operator (no overdispersion). Thus the proportion of this product defects Beta Binomial distribution that arises when p i = p wrong and p i are assumed to have a beta distribution, namely: p i ~ beta (a, b), for a> 0 and b> 0. The purpose of this paper is the result of fundamental research goal is to develop methods that control charts and process capability analysis based Beta Binomial distribution as an alternative to the process capability analysis based on the data distribution Binomial proportion Bremer star product defects. The results of the Beta Binomial control chart Bremer star appears that nothing is out of proportion with the control limit UCL = 0.053884 and LCL= 0.05064, while the individual control chart star chart p-Bremer also no defects proportion out with UCL = 0.7393 and LCL = 0 (less realistic or more in favor of the manufacturer). From the results of the control chart design Bremer star Beta Binomial appears that hose upper control limit and lower control limit is narrower (i.e tighter control chart) than the individual control chart of the p-chart, it is very beneficial for consumers. Based on the analysis capabilities Binomial distribution processes have defective 5.51 percent with the lower limit 5,49 and upper limit 5.52. While the value of 55082 PPM defective in one million products means there are approximately 55082 non-conforming products, with a lower limit of 54 938 and a ceiling of 55227 products. While the results of the analysis Beta Binomial distribution has a defective 5.23 percent with a lower limit of 5.21 and an upper limit of 5.24. While the value of 52264 PPM defective in one million products means there are approximately 52264 non-conforming products, with a lower limit of 52123 and a ceiling of 52405 products. These results indicate that the process capability analysis Beta Binomial distribution has a smaller value of percent defective with a narrower interval compared with the results of the analysis of the ability of the binomial distribution, this will benefit the producers and consumers (the hose tighter).

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hendro Permadi
AU  - Eddy Budiono
AU  - Susy Kuspambudhi
AU  - Ira Nurmawati
PY  - 2017/08
DA  - 2017/08
TI  - Graphics Development Control and Analysis Process Capability Based Distribution Beta Binomial
BT  - Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)
PB  - Atlantis Press
SP  - 219
EP  - 223
SN  - 2352-5398
UR  - https://doi.org/10.2991/icomse-17.2018.18
DO  - 10.2991/icomse-17.2018.18
ID  - Permadi2017/08
ER  -